Extending animation out-of-range by looping, repeat, or cycle
This is possible by using Keyframe Extrapolation, Shift+E in the Graph Editor. This shortcut is also available in the Timeline and Dope Sheet, and you can Ctrl+Tab to quickly access the Graph Editor from any of those panels.

Further, you can change Keyframe Interpolation with T

Finally, you can fine-tune these Modifiers in the Graph Editor under the N menu to restrict their frame range, among other adjustments.